Abstract

A quasiperiodic covering of a plane by regular decagons is described, and an analogous structure in three dimensions is deduced. This consists of a pattern of interpenetrating congruent triacontahedral clusters, related to the tau (3) inflation rule for quasiperiodic Ammann tiling patterns. The overlap regions are triacontrahedron faces, oblate hexahedra, rhombic dodecahedra and rhombic icosahedra. The structure leads to a plausible model for T2 icosahedral quasicrystalline phases.